# Hypersurfaces with parallel affine curvature tensor R*

Barbara Opozda; Leopold Verstraelen

Annales Polonici Mathematici (1999)

- Volume: 72, Issue: 1, page 25-32
- ISSN: 0066-2216

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topOpozda, Barbara, and Verstraelen, Leopold. "Hypersurfaces with parallel affine curvature tensor R*." Annales Polonici Mathematici 72.1 (1999): 25-32. <http://eudml.org/doc/262618>.

@article{Opozda1999,

abstract = {In [OV] we introduced an affine curvature tensor R*. Using it we characterized some types of hypersurfaces in the affine space $ℝ^\{n+1\}$. In this paper we study hypersurfaces for which R* is parallel relative to the induced connection.},

author = {Opozda, Barbara, Verstraelen, Leopold},

journal = {Annales Polonici Mathematici},

keywords = {curvature tensor; induced connection; affine normal; equiaffine normal; Blaschke metric; affine curvature tensor; central quadric},

language = {eng},

number = {1},

pages = {25-32},

title = {Hypersurfaces with parallel affine curvature tensor R*},

url = {http://eudml.org/doc/262618},

volume = {72},

year = {1999},

}

TY - JOUR

AU - Opozda, Barbara

AU - Verstraelen, Leopold

TI - Hypersurfaces with parallel affine curvature tensor R*

JO - Annales Polonici Mathematici

PY - 1999

VL - 72

IS - 1

SP - 25

EP - 32

AB - In [OV] we introduced an affine curvature tensor R*. Using it we characterized some types of hypersurfaces in the affine space $ℝ^{n+1}$. In this paper we study hypersurfaces for which R* is parallel relative to the induced connection.

LA - eng

KW - curvature tensor; induced connection; affine normal; equiaffine normal; Blaschke metric; affine curvature tensor; central quadric

UR - http://eudml.org/doc/262618

ER -

## References

top- [D]₁ R. Deszcz, Pseudosymmetry curvature conditions imposed on the shape operators of hypersurfaces in the affine space, Results Math. 20 (1991), 600-621. Zbl0752.53009
- [D]₂ R. Deszcz, Certain curvature characterizations of affine hypersurfaces, Colloq. Math. 63 (1992), 21-39. Zbl0797.53005
- [NS] K. Nomizu and T. Sasaki, Affine Differential Geometry, Cambridge Univ. Press, 1994.
- [O] B. Opozda, A class of projectively flat surfaces, Math. Z. 219 (1995), 77-92. Zbl0823.53012
- [OS] B. Opozda and T. Sasaki, Surfaces whose images of affine normal are curves, Kyushu Math. J. 49 (1995), 1-10. Zbl0837.53012
- [OV] B. Opozda and L. Verstraelen, On a new curvature tensor in affine differential geometry, in: Geometry and Topology of Submanifolds II, World Sci., 1990, 271-293.
- [VV] P. Verheyen and L. Verstraelen, Locally symmetric affine hypersurfaces, Proc. Amer. Math. Soc. 93 (1985), 101-105. Zbl0535.53007

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